IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v47y2001i8p1101-1112.html
   My bibliography  Save this article

An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution

Author

Listed:
  • Gregory A. Godfrey

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

  • Warren B. Powell

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

Abstract

We consider the problem of optimizing inventories for problems where the demand distribution is unknown, and where it does not necessarily follow a standard form such as the normal. We address problems where the process of deciding the inventory, and then realizing the demand, occurs repeatedly. The only information we use is the amount of inventory left over. Rather than attempting to estimate the demand distribution, we directly estimate the value function using a technique called the Concave, Adaptive Value Estimation (CAVE) algorithm. CAVE constructs a sequence of concave piecewise linear approximations using sample gradients of the recourse function at different points in the domain. Since it is a sampling-based method, CAVE does not require knowledge of the underlying sample distribution. The result is a nonlinear approximation that is more responsive than traditional linear stochastic quasi-gradient methods and more flexible than analytical techniques that require distribution information. In addition, we demonstrate near-optimal behavior of the CAVE approximation in experiments involving two different types of stochastic programs---the newsvendor stochastic inventory problem and two-stage distribution problems.

Suggested Citation

  • Gregory A. Godfrey & Warren B. Powell, 2001. "An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution," Management Science, INFORMS, vol. 47(8), pages 1101-1112, August.
    • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:8:p:1101-1112
    DOI: 10.1287/mnsc.47.8.1101.10231
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.47.8.1101.10231
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.47.8.1101.10231?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    2. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    3. Lau, Hon-Shiang & Hing-Ling Lau, Amy, 1996. "Estimating the demand distributions of single-period items having frequent stockouts," European Journal of Operational Research, Elsevier, vol. 92(2), pages 254-265, July.
    4. P C Bell, 2000. "Forecasting demand variation when there are stockouts," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(3), pages 358-363, March.
    5. David J. Braden & Marshall Freimer, 1991. "Informational Dynamics of Censored Observations," Management Science, INFORMS, vol. 37(11), pages 1390-1404, November.
    6. Suvrajeet Sen & Julia L. Higle, 1999. "An Introductory Tutorial on Stochastic Linear Programming Models," Interfaces, INFORMS, vol. 29(2), pages 33-61, April.
    7. Linos F. Frantzeskakis & Warren B. Powell, 1990. "A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems," Transportation Science, INFORMS, vol. 24(1), pages 40-57, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kevork, Ilias S., 2010. "Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions," Omega, Elsevier, vol. 38(3-4), pages 218-227, June.
    2. Halkos, George & Kevork, Ilias, 2011. "Non-negative demand in newsvendor models:The case of singly truncated normal samples," MPRA Paper 31842, University Library of Munich, Germany.
    3. Raymond K.-M. Cheung & Warren B. Powell, 2000. "Shape -- A Stochastic Hybrid Approximation Procedure for Two-Stage Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 73-79, February.
    4. Halkos, George & Kevork, Ilias, 2012. "Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand," MPRA Paper 36460, University Library of Munich, Germany.
    5. Ulrich, Matthias & Jahnke, Hermann & Langrock, Roland & Pesch, Robert & Senge, Robin, 2021. "Distributional regression for demand forecasting in e-grocery," European Journal of Operational Research, Elsevier, vol. 294(3), pages 831-842.
    6. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand," MPRA Paper 39650, University Library of Munich, Germany.
    7. Gregory D. Glockner & George L. Nemhauser, 2000. "A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure," Operations Research, INFORMS, vol. 48(2), pages 233-242, April.
    8. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand," MPRA Paper 36205, University Library of Munich, Germany.
    9. Gen Sakoda & Hideki Takayasu & Misako Takayasu, 2019. "Data Science Solutions for Retail Strategy to Reduce Waste Keeping High Profit," Sustainability, MDPI, vol. 11(13), pages 1-30, June.
    10. Abdel-Malek, Layek L. & Areeratchakul, Nathapol, 2007. "A quadratic programming approach to the multi-product newsvendor problem with side constraints," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1607-1619, February.
    11. Boutselis, Petros & McNaught, Ken, 2014. "Finite-Time Horizon Logistics Decision Making Problems: Consideration of a Wider Set of Factors," Chapters from the Proceedings of the Hamburg International Conference of Logistics (HICL), in: Blecker, Thorsten & Kersten, Wolfgang & Ringle, Christian M. (ed.), Innovative Methods in Logistics and Supply Chain Management: Current Issues and Emerging Practices. Proceedings of the Hamburg International Conferenc, volume 19, pages 249-274, Hamburg University of Technology (TUHH), Institute of Business Logistics and General Management.
    12. Aditya Jain & Nils Rudi & Tong Wang, 2015. "Demand Estimation and Ordering Under Censoring: Stock-Out Timing Is (Almost) All You Need," Operations Research, INFORMS, vol. 63(1), pages 134-150, February.
    13. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, I: Single Period Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 21-39, February.
    14. Warren B. Powell, 2016. "Perspectives of approximate dynamic programming," Annals of Operations Research, Springer, vol. 241(1), pages 319-356, June.
    15. Mofidi, Seyed Shahab & Pazour, Jennifer A. & Roy, Debjit, 2018. "Proactive vs. reactive order-fulfillment resource allocation for sea-based logistics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 66-84.
    16. Raymond K. Cheung & Chuen-Yih Chen, 1998. "A Two-Stage Stochastic Network Model and Solution Methods for the Dynamic Empty Container Allocation Problem," Transportation Science, INFORMS, vol. 32(2), pages 142-162, May.
    17. Jingxian Chen & Liang Liang & Dong-Qing Yao, 2017. "Pre-positioning of relief inventories for non-profit organizations: a newsvendor approach," Annals of Operations Research, Springer, vol. 259(1), pages 35-63, December.
    18. Ramaekers Katrien & Caris An & Maes Tabitha & Janssens Gerrit K., 2015. "Pickup and Delivery Selection: Problem Formulation and Extension to Problem Variants," Information Technology and Management Science, Sciendo, vol. 18(1), pages 84-90, December.
    19. Sarhadi, Hassan & Naoum-Sawaya, Joe & Verma, Manish, 2020. "A robust optimization approach to locating and stockpiling marine oil-spill response facilities," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    20. Schulte, Benedikt & Sachs, Anna-Lena, 2020. "The price-setting newsvendor with Poisson demand," European Journal of Operational Research, Elsevier, vol. 283(1), pages 125-137.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:47:y:2001:i:8:p:1101-1112. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.